The first symbol that comes to mind is a balloon, which represents the rises and falls (literally and figuratively) in the Professor's story, getting him off the ground, crashing him on the island, and then providing his and others' rescue when the volcano erupts.
A second symbol that comes to mind is the seagull that is responsible for his forced landing. It represents to some degree the idea that man cannot triumph over nature, and it brings to mind the albatross, which is a rather famous symbol in the poem "The Rime of the Ancient Mariner" (Coleridge), a poem you might enjoy reading. The albatross is a central element and symbol in that poem.
A third symbol, for me, is the diamonds, which represent man's greed, although it is wonderful to read a story in which people finally cooperate fully and do not give in to greed.
Finally, the volcano is a symbol of man's ability to harness nature, but ultimately, to not be able to control it.